Problem: Rewrite as a simplified fraction. ${3.7\overline{5} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 375.5555...\\ 10x &= 37.5555...\end{align*}}$ Subtracting the two equations, we have: ${90x = 338}$ ${x = \dfrac{338}{90}} $ ${x = \dfrac{169}{45}} \text{or} {3 \dfrac{34}{45}}$